In deliberating on the outcomes of Washington's misadventures in Iraq and Afghanistan, a strategy of analysis that many Washington pundits use is to prefer 'incompetence' over 'conspiracy' ("They really wanted to spread democracy, but they messed up!"). But below I quote an interview clip of Dick Cheney from 1994 which shows that the Neocons clearly knew what would happen in Iraq. And, not just that, I believe they knew the fault lines (polarized and exacerbated by Saddam's neo-tribal and sectarian policies) and pro-actively exploited them to create instability in the country to justify their prolonged presence (A close scrutiny of Paul Bremer's policies immediately after the occupation and of the presence of John Negroponte and Blackwater would provide ample illuminations. Washington did at first flirt with the idea of installing the puppet Ahmed Chalabi, while utilizing the ongoing instability as the pretext for its longer stay, but the plan failed due to Iraq's Ayatollah Ali Sistani's timely intervention calling for open elections in 2005.)
A longer stay in Iraq not only had financial incentives for the military-industrial complex, but also was crucial for Washington's long-term hegemonic ambitions for the region. (It is for similar reasons that Washington wants to maintain its presence in the so-called "Af-Pak" region. Having Obama in the White House hasn't 'changed' anything.)
But perhaps it was Israel that hoped to benefit the most from the instability in Iraq. Since at least 1967, Israel has followed the policy of carrot-and-stick, co-opting the cooperative Arab regimes (like Anwar Sadat's Egypt with the Camp David Accord in 1978 which was facilitated by Washington's aid in billions of dollars), and dividing and destabilizing the non-cooperative states. As a strategic policy for its immediate neighbors, Israel has persistently sought to see them politically and economically weak and preoccupied within themselves. That was one of the reasons why Israel indiscriminately bombarded the basic infrastructure and economically viable facilities in Beirut (and the rest of the country) in the Summer 2006. (The other reason was to turn the Lebanese factions against the resistance movement.) It was also Israel that in its air strike on June 7, 1981 destroyed an Iraqi nuclear plant near Baghdad and then tried to justify that as an act of "self-defense".
The first benefit that Israel hoped to see with the American invasion was an even weaker and fragmented Iraq (which would also destabilize Turkey, Iran, KSA, Syria, Lebanon). The second was a continued presence of American forces in the region. The third was the convergence of Israeli and Neocons' interest in targeting Iran, as they surely hoped that the road to Tehran went through Baghdad.
However, their plans did not always bear the fruits they desired.